1. Introduction

In the recent years, King County, WA has experienced major population growth, largely due to its thriving economy. Being the home county to many industry-leading companies, such as Microsoft, Amazon, Boeing, and Starbucks, King County is injected with an influx of talented individuals come to work for those companies. This workforce boosts the County’s economy while it also raises the rapid-growing needs of infrastructure and housing development. In the meantime, working in accordance with Washington State’s Growth Management Act, King County has successfully adopted its own Growth Management Act to protect natural resources, rural lands and other critical areas and grow with an increasing urban density simultaneously. The population growth in the County is still growing rapidly, especially with Amazon’s headquarter continuously attracting more and more incoming workforce.

Recognising the need for both growth and environmental preservation, this project first forecasts demand for urban growth and development by considering the effects of population growth and infrastructure provision. Specifically, the latter projection scenario will consider the expansion of the metro network in King County. Then, an analysis of sensitive lands will be carried out to understand where urban growth should not encroach. Based on these two angles of consideration, recommendations will be made for where the Board could allocate for and promote further development.

2. Forecasting Urban Growth Demand

To forecast urban growth demand, it is useful to consider previous urban growth patterns, and how they relate to underlying land cover, population, and transportation patterns. Notably, population growth can spur urban growth naturally, as more space is required to provide housing for a larger population. Likewise, transportation networks like roads and public transit often induce further development and urban growth, as places made more accessible via such links are activated as places for housing and industries.

To predict urban growth demand for 2020, the case of land cover change between 2001 and 2011 is analysed. Specifically, land cover, population, and transportation patterns during this period are used to model this period of land cover change (Section 2.1). Based on this model, the urban growth demand for 2020 is then predicted for (Section 2.2).

To parameterize such spatial relationships in a regression context, a vector fishnet is employed - each grid cell can then be treated as a single data point for which the prediction is made. Each grid cell in the fishnet represents a 4000ft by 4000ft area (Figure 1) within King County. There are 4040 grid cells in total. Land cover change, land cover, population, and transportation variables, or features, are then integrated with the grid cells spatially associated with them.

Figure 1: King County by way of fishnet

2.1 Modeling Urban Growth Demand (2001 - 2011)

2.1.2 Exploratory analysis of features

A) Dependent variable: Land cover change

Here, the dependent variable we wish to forecast is land cover change between 2001 and 2011. For this section, the land cover change raster data was loaded, reclassified, and integrated with a vector fishnet. It can be observed (Figure 2) that the bulk mass of land cover change during this period occurred West of the County. Based on this, it could be said that there is generally a east-west divide in urban growth outcomes observed in 2011 for King County. There are pockets of development extending from this mass eastwards - this imply that there may be local characteristics that spurred development at these locations but not at neighbouring ones.

Figure 2: Land Cover Change (2001 - 2011)

B) Predictive feature: Land cover patterns 2001

It is reasonable to hypothesize that the propensity for new development is a function of existing land over categories. Again, for this section, the land cover raster data was loaded, reclassified, and integrated with a vector fishnet. The table below shows the approach taken to recode existing land cover codes into the categories used in our analysis.

NLCD Classification	New Classification
Open Space as well as Low, Medium, and High Intensity Development	Developed
Water and emergent herbaceous wetlands	Wetlands
Woody wetlands, shrubs, and grassland/herbaceous	Woodlands
Deciduous, evergreen and mixed forests	Forest
Pasture, hay, and cultivated crops	Farm

It can be observed from the maps below (Figure 3) that there are substantial overlaps between different land cover patterns. This is in part due to the grid-based reclassification - a grid cell may overlap with adjacent areas of different land cover types, and are thus integrated with more than a single land cover type. Given the substantial overlaps, these features can be considered to exhibit similar spatial patterns, and it is likely that these features are multicollinear. In other words, it might not be useful to include all land cover type features as possible predictors for land cover change. It might be more effective to choose specific features that could be used to estimate for the overall land cover change instead, based on observed associations between land cover change and each land cover type.

Figure 3: Land Cover Types (2001)

To determine if there might be an association between land cover change and each land cover type, the proportion of each land cover type area that experienced land cover change is calculated. It could then be noted that land cover change occurred for 55.6% of farm areas in King County - the largest proportion out of all land cover types. Spatially, it could also be observed that farm areas which experienced land cover change are also located at the peripheral (sprawl) regions of the total land cover change area - this feature could be helpful in helping the model detect grid cells which might experience land cover change but are not located near to the main tracts of land cover change.

C) Predictive feature: Population patterns 2000-2010

It is also reasonable to hypothesize that new development is driven by existing population trends. Here, it is interesting to consider whether the population pattern before 2001 or the overall population change trend between 2000 and 2010 could have driven the development trend manifested in 2011. Both features are therefore compared (Figure 4).

Figure 4: Population trends (2000)

On the overall, it could be noted that there was not much subtantial change in population numbers during the period on the overall, or noticeable spatial concentrations of distinct population change. Conversely, the difference in population between areas of land cover change and no change is much more stark, suggesting that this feature might be a more suitable predictor for land cover change.

D) Predictive feature: Transportation network patterns 2001

Transportation can be regarded as form of supply-induced demand for development, manifested as land cover change. This is because transportation links connect people and goods to places, making industries dependent on people and goods exchange to thrive. This provides the impetus for urban development at otherwise distant places.

Again, there are many types of transportation network links, such as road networks and metro networks. To determine which may have a greater association with areas of land cover change, the spatial distribution of distances to such networks are compared, along with the average distances between transport networks and areas which may or may not have experienced land cover change (Figure 5).

Figure 5: Transportation network patterns (2001)

It could be observed that areas which experienced land cover change are located very close to the road network.The spatial patterns of distances to the metro hubs and light rail stations are similar. However, as areas which experienced land cover change are generally located closer to metro hubs, the distance to metro hubs may be a more useful predictor of land cover change instead.

2.1.2 Fitting the model for 2011

Different logistic regression models were estimated to predict development change between 2001 and 2011 using different combinations of the features presented in the previous section. To do so, the data was split into 50% training and test sets. Models were estimated on the training set.

For brevity sake, the McFadden or ‘Pseudo’ R-square statistic was computed for the test set for each model. The model with the greatest goodness of fit by this metric was the one that predicted land cover change using the features of presence of farm land, population in 2000, distance to metro hubs, and distance to roads. The figure below presents the distribution of test set predicted probabilities.

Figure 6: Distribution of test set predicted probabilities

The addition of other factors to these 4 features only compounded the issue of multicollinearity - in order words, the other features do not add much more predictive value to the model. Therefore, this model is further evaluated in terms of accuracy and spatial generalisability in the section below.

2.1.3 Evaluating the model for 2011

Choice of threshold probability to optimise accuracy Given that the logistic model predicts a continuous range of development probabilities, a single probability threshold should be picked to classify an area as having or not having new development. To pick a suitable probability threshold, we consider the distribution of confusion types (see table) at different probability thresholds.

Confusion Type	Interpretation
True positive	Land cover change occurred, and is correctly predicted to have occured.
True negative	Land cover change did not occur, and is correctly predicted to not have occured.
False positive	Land cover change did not occur, but is incorrectly predicted to have occured.
False negative	Land cover change occurred, but is incorrectly predicted to not have occured.

Based on these confusion types, we can also interpret the accuracy of the model in terms of:

• Misclassification rate: This refers to the rate at which false negative and false positive predictions were made.
• Sensitivity: This refers to the proportion of land cover change events that were correctly identified. In other words, it also approximates the ratio between true positive rates and false negative rates.
• Specificity: This refers to the proportion of land cover change non-events that were correctly identified. In other words, it also approximates the ratio between true negative rates and false positive rates.

Two kinds of probability thresholds are usually considered. The first type of probability threshold minimises misclassification rate - this maximises overall accuracy. The second type maximises both sensitivity and specificity rates, and not necessarily overall accuracy. The figure (Figure 7) below highlights where these two probability thresholds lie in the distribution of confusion types at different probability thresholds.

Figure 7: Distribution of confusion types at different probability threshold points

A comparison of the spatial accuracy of these two probability thresholds (Figure 8) reveals that the threshold that maximises specificity and sensitivity yields predictions that account for development at areas extending beyond the western region of King County. On the other hand, the threshold that minimises misclassification rate yields predictions that are more conservative - while it yields a much lower false positive rate, it also fails to predict for development in areas further away from the western region of King County.

Figure 8: Comparing Prediction Probability Thresholds in terms of Confusion Types

From a planning perspective, it could be argued that it is more important to accurately detect development in regions further away from the presently-developed or popularly-developed area. This allows planning attention to be directed to such otherwise-overlooked areas, in order to ensure that development is carried out in an economically and environmentally-sustainable manner. Therefore, the lower probability threshold of 0.31 (that maximises sensitivity and specificity) is chosen as the final cut-off between development and non-development outcomes. The figure below shows how this choice not only maximises sensitivity and specificity, its resulting misclassification rate also does not substantially deviate from the minimum rate possible at a higher threshold.

Figure 9: Distribution of classification outcomes across threshold cut-offs

Evaluating spatial generalisability

Based on this probability threshold of 0.31, it is important to ensure that errors in terms of false positive and false negative events are evenly distributed across space. In other words, the model should accurately predict for development for different areas, in this case districts, in King County.

Based on the figure below however, it could be observed that such errors are clustered along the western boundary between the generally developed regions and the more-rural sections of King County. This means that there the most western and eastern districts enjoy the highest accuracy rates, given that such districts are often either entirely developed or not developed. It is the districts that lie along this boundary that experience mixed accuracy rates, as apparent from both the map and bar plots in the figure below.

Figure 10: Distribution of Confusion Types across King County

2.2 Predicting Urban Growth Demand in 2020

Using the model trained in the previous section, we predict development demand for 2020 based on presence of farmland, population 10 years ago, distance to metro hubs, and distance to roads.

To do this, we update the features to reflect the underlying situation 10 years before 2020. Specifically, the features for farm cover and population are updated to reflect the 2011 situation. As no new roads were built during this period, the distance to roads remain the same.

Here, we consider two different scenarios involving the metro network that would likely result in different development demand. The first assumes that no new metro hubs were built during this period - distance to metro hubs therefore remains the same. The second considers the implementation of the metro hub expansion plans - with the inclusion of new metro hub stations, the distance to metro hubs may change for some areas in King County. For this scenario, it is likely that this infrastructure supply might induce more development - we shall hence refer to this as supply-induced development in the discussion in this section.

The figure below (Figure 11) presents the locations of current and planned metro hubs. It could be observed that the planned metro hubs further extend beyond the main developed region in the west side of King County, indicating that development demand could be induced beyond this area.

Figure 11: Current and Planned Metro Hubs

The current metro transit hubs which marked in blue are nodes where different modes of public transit gather. The proposed six new metro transit hubs, marked in red, are planned with the idea to expand the public transit system in King County in the most cost-effective way. Since the nature of topography and land cover in the area and the constraint of the budget, it is unrealistic to expand the Link Light Rail system to Vashon Island (the leftmost point) or Snoqualmie Falls (the rightmost point). Building transit hubs and designate bus routes accordingly will be a more realistic to grow the regional transit network and facilitating the increasing population’s housing and transportation needs.

Comparing the predicted development demand outcomes for these two scenarios, it could indeed be observed that development demand potential is higher beyond the west-side of the county when new metro hubs are included in consideration of urban growth in 2020. The extended limb of higher development demand due to additional transit infrastructure supply is stretched further eastward, increasing the development demand of areas around it as well. Therefore, urban growth is likely to be more widespread in the scenario where new metro hubs are included. In other words, the Board can consider spurring urban growth in undeveloped areas through transit-oriented development.

Figure 12: Predicted Development Demand Outcomes

3. Environmental Sensitivity Analysis

According to the sensitivity analysis (Figure 13), the region’s sensitive land lost has been fairly minimal, largely thanking to the King County Growth Management Act adopted in 1994. King County has focused on preserving natural lands by making 97% of new residential constructions happen within designated Urban Centers. This action is what leads King County to a sustainable future. Therefore, in the following section, not only the analysis reflects such a “develop but preserve” rationale, the planning recommendations that we propose also maintain such an effort as the focus.

Figure 13: Sensitive Lands Lost

4. Allocating Development

In the development allocation analysis, we used the school districts instead of political boundaries as the demarcations to cut out different study areas (Figure 14). The rationale behind that is to look into the allocation of development through a more people-oriented lens. And the outcomes of different types of development demand (supply-induced and non-supply-induced) are consistent of the characteristics of each district, which we will select a couple of key districts and dive into more detailed explanation in the later sections. Overall, non-rural districts (Enumclaw, Riverview, Skykomish, and Tahoma) expect to have a lot less development demand (as shown in the black bars) than all the other districts. Vashon Island district also has less predicted development demand potentially due to its geographic location.

Figure 14: District Specific Allocation Metrics

However, before looking at the predicted development potential, it is worth noting that King County has abundant natural assets and is largely covered by forest (Figure 15). This results in the majority area that is undeveloped is categorized as not suitable for development. Once again, to reference to the King County Growth Management Act, we, therefore, will make planning recommendations with the respect of preserving the natural assets.

Figure 15: Selected Land Cover Types in 2011

Bellevue and Seattle

Both economics of the two districts are booming and all the area in the two districts are developed. In addition, the two districts are both expecting to have very high development demand. Therefore, infill development and increasing urban density becomes the one and only way to accommodate the future growth in the areas. One interesting thing is that even though the East side of Bellevue and the South side of Seattle are expected to have population decrease between 2010 and 2020, both of these areas still show high development demand. This phenomenon could be the response to the growing districts East of Bellevue and South of Seattle, which will be investigated in the next section.

Figure 16: Allocating Development in Bellevue and Seattle

Issaquah, Aurburn and Renton Issaquah is located east of Bellevue whereas Renton and Auburn are south of Seattle. With the influx of tech population to Seattle and Bellevue in the recent years, many people have moved to these surrounding districts for lower density and cheaper housing, yet still convenient work commutes. Therefore, we suggest to develop in the North and East part of Issaquah and Auburn, preserving the forest lands in the middle of Issaquah while plan even more developments in Renton so that it is going to be not just a satellite area to Seattle but its own regional center.

Figure 17: Allocating Development in Issaquah, Auburn and Renton

Enumclaw and Snoqualmie Valley These two areas are more remote and contain rural characteristics comparing to other districts. Since it is crucial for King County to keep its rural characteristics while accommodating the growth of its economy and population, we recommend to develop the least in these two areas. The predicted development potential and demand also backs up this suggestion since these the majority of the two districts are not suitable for development and the development demands are very low.

Figure 18: Allocating Development in Enumclaw and Snoqualmie Valley

5. Conclusion

King County is a place with urgent need for development to accommodate its growth. Nevertheless, it is a place puts a lot emphasis on the sustainable development, for instance, its adoption of a Growth Management Acts for the past 25 years. The outcome is the development needs to be allocation with extra scrutiny so that it can maximize an area’s potential. And the above-mentioned recommendations are built upon such rationale and recommend the County to continuously densify the major urban centers, such as Seattle and Bellevue, with additional effort to focus more developments on surrounding districts, such as Issaquah, Renton, and Auburn, while keep preserving the rural identity of districts like Enumclaw and Snoqualmie Valley.